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Positive feedbacks in climate processes can make it difficult to identify the primary drivers of climate phenomena. Some recent global climate model (GCM) studies address this issue by controlling the wind stress felt by the surface ocean such that the atmosphere and ocean become mechanically decoupled. Most mechanical decoupling studies have chosen to override wind stress with an annual climatology. In this study we introduce an alternative method of interannually varying overriding which maintains higher frequency momentum forcing of the surface ocean. Using a GCM (NCAR CESM1), we then assess the size of the biases associated with these two methods of overriding by comparing with a freely evolving control integration. We find that overriding with a climatology creates sea surface temperature (SST) biases throughout the global oceans on the order of ±1°C. This is substantially larger than the biases introduced by interannually varying overriding, especially in the tropical Pacific. We attribute the climatological overriding SST biases to a lack of synoptic and subseasonal variability, which causes the mixed layer to be too shallow throughout the global surface ocean. This shoaling of the mixed layer reduces the effective heat capacity of the surface ocean such that SST biases excite atmospheric feedbacks. These results have implications for the reinterpretation of past climatological wind stress overriding studies: past climate signals attributed to momentum coupling may in fact be spurious responses to SST biases. Plain Language Summary: Because the ocean influences the atmosphere and vice versa, chicken‐or‐egg type problems abound throughout the climate system. Some studies have addressed this by controlling the wind stress field felt by the ocean in climate models in order to mechanically decouple the ocean from the atmosphere and thus determine the surface ocean response to a change in momentum forcing. Most previous studies that override wind stress have fed the ocean a mean annual cycle; however, this method removes the effect of shorter‐term events like storms. We compare how well overriding experiments, forced either with the mean annual cycle of wind stress or with year‐to‐year varying wind stress, agree with a freely evolving control simulation. We find substantially larger sea surface temperature biases in the simulation forced with the mean annual cycle of wind stress. We attribute these biases to the lack of short‐term weather events which mix the surface ocean. Key Points: Most previous wind stress overriding simulations have disabled momentum feedbacks in global climate models by overriding with a climatologyWe introduce a protocol to override with interannually varying wind stress, which leads to smaller biases than climatological overridingWe attribute this difference to a lack of synoptic variability in climatological overriding which shoals the mixed layer [ABSTRACT FROM AUTHOR]